A254569 The number of unordered pairs (f,g) of functions from {1..n} to itself such that fg=gf (i.e., f(g(i))=g(f(i)) for all i).

1, 7, 84, 1540, 37345, 1145376, 42402871, 1849021504, 93217426857, 5363120671120, 348669188664511, 25418305492373520, 2064813985107357445, 185896884170249831320, 18459391640792004885375, 2012607682674617326564096, 239898601216105901349115537, 31132586664410794285693925664, 4380971763246528510240944123071, 665896706682993760478978112600400

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

a(n) = (A181162(n) - n^n)/2 + n^n.

Example

The a(2) = 7 pairs of maps [2] -> [2] are:
01:  [ 1 1 ]  [ 1 1 ]
02:  [ 1 1 ]  [ 1 2 ]
03:  [ 1 2 ]  [ 1 2 ]
04:  [ 1 2 ]  [ 2 1 ]
05:  [ 1 2 ]  [ 2 2 ]
06:  [ 2 1 ]  [ 2 1 ]
07:  [ 2 2 ]  [ 2 2 ]

Crossrefs

Cf. A181162 (ordered pairs), A254570 (unordered pairs, f and g distinct).

Sequence in context: A172455 A258174 A370934 * A183177 A367351 A058795

Adjacent sequences: A254566 A254567 A254568 * A254570 A254571 A254572

Keyword

nonn

Author

Joerg Arndt, Feb 01 2015

Status

approved